KCGT-MEM: Interface-Prior Maximum Entropy Reconstruction — Hierarchy, Regime Map, and the Lagged-Diffusivity Estimator (paper, code, and data)

Software, data, and manuscripts for the KCGT-MEM framework, which integrates the KCGT interface/boundary concept into Maximum Entropy Method image reconstruction within the Mumford-Shah / edge-enhancing-diffusion functional family (levels L0-L3). The deposit contains the main paper and a cosmological companion note, the complete matched-comparison code (accelerated L3 solver, field generators, and experiment drivers), per-seed result archives, and all figures. New in this version: a decomposition of the lagged-diffusivity estimator's self-amplifying feedback into an orientation channel and a contrast/eigenvalue channel, the finding that the dense-sampling edge of the applicable regime is a property of the eigenvalue estimator rather than of the prior, a task-dependent operating rule (morphometric vs topological), and an application to synthetic medical phantoms showing that eigenvalue anchoring removes the entropy-overshoot lumen-diameter under-estimation at the cost of continuity bridging. Seeds are fixed so all comparisons are paired and every reported statistic is recomputable from the archives.